Question

a first number plus twice a second number is 22. twice the first number plus the second totals 17. find the numbers. the smaller of the two numbers is . the larger of the two numbers is .

Explanation:

Step1: Let the first number be $x$ and the second number be $y$.

Set up the equations: $x + 2y=22$ and $2x + y = 17$.

Step2: Multiply the first - equation by 2.

We get $2x+4y = 44$.

Step3: Subtract the second equation from the new - formed equation.

$(2x + 4y)-(2x + y)=44 - 17$. Simplify to get $3y=27$, so $y = 9$.

Step4: Substitute $y = 9$ into the first equation.

$x+2\times9=22$, which is $x+18 = 22$. Then $x=22 - 18=4$.
Since $9>4$, the larger number is 9 and the smaller number is 4.

Answer:

The larger of the two numbers is 9.
The smaller of the two numbers is 4.